×
Shen, Hao; Xu, Shengyuan; Lu, Junwei; Zhou, Jianping

Passivity-based control for uncertain stochastic jumping systems with mode-dependent round-trip time delays. (English) Zbl 1254.93148

J. Franklin Inst. 349, No. 5, 1665-1680 (2012).
Summary: This paper considers the passivity-based control problem for stochastic jumping systems with mode-dependent round-trip time-varying delays and norm-bounded parametric uncertainties. By utilizing a novel Markovian switching Lyapunov functional, a delay-dependent passivity condition is obtained. Then, based on the derived passivity condition, a desired Markovian switching dynamic output feedback controller is designed, which ensures that the resulting closed-loop system is passive. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed results.

Cited in 76 Documents

MSC:

93E03 Stochastic systems in control theory (general)
93B35 Sensitivity (robustness)
60J75 Jump processes (MSC2010)

Keywords:

mode-dependent round-trip time-varying delays; novel Markovian switching Lyapunov functional; dynamic output feedback controller; delay-dependent passivity condition; passivity-based control problem; norm-bounded parametric uncertainties; closed-loop system
PDF BibTeX XML Cite
\textit{H. Shen} et al., J. Franklin Inst. 349, No. 5, 1665--1680 (2012; Zbl 1254.93148)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Basin, M.V.; Rodriquez-Gonzalez, J.; Martinez-Zuniqua, R., Optimal filtering for linear state delay systems, IEEE transactions on automatic control, 50, 684-690, (2005) · Zbl 1365.93496
[2] Basin, M.V.; Shi, P.; Calderon-Alvarez, D., Central suboptimal \(H_\infty\) filter design for linear time-varying systems with state and measurement delay, International journal of systems science, 42, 801-808, (2011) · Zbl 1233.93029
[3] Boukas, E.K., Stabilization of stochastic nonlinear hybrid systems, International journal of innovative computing, information and control, 1, 131-141, (2005) · Zbl 1085.93026
[4] Cao, Y.-Y.; Lam, J.; Hu, L., Delay-dependent stochastic stability and \(H_\infty\) analysis for time-delay systems with Markovian jumping parameters, Journal of franklin institute, 340, 423-434, (2003) · Zbl 1040.93068
[5] Ding, Q.; Zhong, M., On designing \(H_\infty\) fault detection filter for Markovian jump linear systems with polytopic uncertainties, International journal of innovative computing, information and control, 6, 995-1004, (2010)
[6] Fridman, E.; Shaked, U., On delay-dependent passivity, IEEE transactions on automatic control, 47, 664-669, (2002) · Zbl 1364.93370
[7] Y. Fu, G. Duan, Stochastic stabilizability and passive control for time-delay systems with Markovian jumping parameters, in: Eighth International Conference on Control, Automation, Robotics and Vision, Kunming, China, December 2004, pp. 1757-1761.
[8] Hodgson, S.; Stoten, D.P., Passivity-based analysis of the minimal control synthesis algorithm, International journal of control, 63, 67-84, (1996) · Zbl 0854.93055
[9] Lam, J.; Gao, H.; Wang, C., Stability analysis for continuous systems with two additive time-varying delay components, Systems & control letters, 56, 16-24, (2007) · Zbl 1120.93362
[10] Li, H.; Gao, H.; Shi, P., New passivity analysis for neural networks with discrete and distributed delays, IEEE transactions on neural networks, 21, 1842-1847, (2010)
[11] Li, H.; Wang, C.; Shi, P.; Gao, H., New passivity results for uncertain discrete-time stochastic neural networks with mixed time delays, Neurocomputing, 73, 3291-3299, (2010)
[12] Li, H.; Zhou, Q.; Chen, B.; Liu, H., Parameter-dependent robust stability for uncertain Markovian jump systems with time delay, Journal of franklin institute, 348, 738-748, (2011) · Zbl 1227.93126
[13] Lin, C.; Wang, Q.-G.; Lee, T.H., A less conservative robust stability test for linear uncertain time-delay systems, IEEE transactions of automatic control, 51, 87-91, (2006) · Zbl 1366.93469
[14] Mahmoud, M.S., Passivity and passification of jump time-delay systems, IMA journal of mathematical control & information, 23, 193-209, (2006) · Zbl 1095.93017
[15] Mao, X., Exponential stability of stochastic delay interval systems with Markovian switching, IEEE transactions on automatic control, 47, 1604-1612, (2002) · Zbl 1364.93685
[16] Nakura, G., Stochastic optimal tracking with preview by state feedback for linear discrete-time Markovian jump systems, International journal of innovative computing, information and control, 6, 15-28, (2010)
[17] Sha Sadeghi, M.; Momeni, H.R.; Amirifar, R., \(H_\infty\) and \(L_1\) control of a teleoperation system via lmis, Applied mathematics and computation, 206, 669-677, (2008) · Zbl 1152.93358
[18] Shao, H., Delay-range-dependent robust \(H_\infty\) filtering for uncertain stochastic systems with mode-dependent time delays and Markovian jump parameters, Journal of mathematical analysis and applications, 342, 1084-1095, (2008) · Zbl 1141.93025
[19] Shen, H.; Xu, S.; Zhou, J.; Lu, J., Fuzzy \(H_\infty\) filtering for nonlinear Markovian jump neutral systems, International journal of systems science, 42, 767-780, (2011) · Zbl 1233.93091
[20] Shen, H.; Chu, Y.; Xu, S.; Zhang, Z., Delay-dependent \(H_\infty\) control for jumping delayed systems with two Markov processes, International journal of control, automation, and systems, 9, 437-441, (2011)
[21] Shi, P.; Boukas, E.K.; Agarwal, R.K., Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters, IEEE transactions on automatic control, 44, 1592-1597, (1999) · Zbl 0986.93066
[22] Wang, G.; Zhang, Q.; Sreeram, V., \(H_\infty\) control for discrete-time singularly perturbed systems with two Markov processes, Journal of franklin institute, 347, 836-847, (2010) · Zbl 1286.93194
[23] Xia, Y.; Zhu, Z.; Mahmoud, M., \(H_2\) control for networked control systems with Markovian data losses and delays, ICIC express letters, 3, 271-276, (2009)
[24] Xu, S.; Chen, T.; Lam, J., Robust \(H_\infty\) filtering for uncertain Markovian jump systems with mode-dependent time delays, IEEE transactions on automatic control, 48, 900-907, (2003) · Zbl 1364.93816
[25] Xu, S.; Lam, J.; Mao, X., Delay-dependent \(H_\infty\) control and filtering for uncertain Markovian jump systems with time-varying delays, IEEE transactions on circuits and systems I: regular papers, 54, 2070-2077, (2007) · Zbl 1374.93134
[26] Yin, Y.; Shi, P.; Liu, F., Gain-scheduled PI tracking control on stochastic nonlinear systems with partially known transition probabilities, Journal of franklin institute, 348, 685-702, (2010) · Zbl 1227.93127
[27] Zhang, J.; Shi, P.; Qiu, J., Non-fragile guaranteed cost control for uncertain stochastic nonlinear time-delay systems, Journal of franklin institute, 346, 676-690, (2009) · Zbl 1298.93364
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.